RTG at The Ohio State University
| Award | Undergraduate | Graduate | Postdoctoral | People | RTG Workshop and Retreat | Outcomes |
DAVID ANDERSON works in algebraic geometry, with connections to combinatorics and representation theory of Lie groups. He is particularly interested in using group actions and techniques from equivariant cohomology to relate modern combinatorics with classical enumerative geometry.
SERGEI CHMUTOV's research interests and activities lie in the area of combinatorics arising from the theory of knots and links. His current projects include the study of weight systems coming from the Lie algebra glN, the weight systems coming from combinatorics of ribbon graphs and their mutual relationships. Also, he run a REU-like summer program "Knots and Graphs", where students are involved into research in my field.
JAMES COGDELL works in number theory, particularly the theory of automorphic representations and their L-functions; this is the global analytic side of the Langlands program. Locally, he is interested in Bessel functions of representations and their relations to local constants.
MARIA ANGELICA CUETO works in combinatorial algebraic geometry, with particular emphasis in tropical and non-Archimedean geometry. Her current projects encompass the topology of surface singularities and computational methods for studying spaces of valuations on classical varieties and their moduli spaces through their initial (tropical) degenerations.
SACHIN GAUTAM works on representation theory of infinite-dimensional quantum groups: Yangians, quantum loop algebras and elliptic quantum groups. He specializes in using analytic methods (asymptotic analysis, Borel resummation) from the theory of difference equations to construct explicit connections among these quantum groups.
GHAITH HIARY works in works in computational and analytic number theory. Topics include the theory of the Riemann zeta function, Dirichlet L-functions, exponential sums, number theoretic algorithms, and asymptotics motivated by moment problems from number theory and random matrix theory.
ERIC KATZ studies the interplay between combinatorics and algebraic geometry, with applications to number theory. He uses ideas from tropical geometry to transform questions in algebraic geometry into questions in combinatorics through the combinatorial study of degenerations and stratifications.
MICHAEL LIPNOWSKI works in number theory, at the nexus of all aspects - arithmetic, spectral geometry, topology, etc. - of locally symmetric spaces. His current projects include p-adic approaches to complex multiplication for non CM number fields and algorithms for building grids on locally symmetric spaces.
WENZHI LUO is interested in analytic methods and techniques in the studies of arithmetic of automorphic forms, especially arithmetic statistics and quantitative results on the special values of automorphic L-functions, as well as their applications in geometry and arithmetic.
HOI NGUYEN's primary interests include combinatorics and random matrix theory. More specifically, he is interested in additive, algebraic and probabilistic combinatorics. Within random matrix theory, he is interested in universality behavior of spectral and algebraic statistics, as well as in integrable probability.
JENNIFER PARK is interested in the study of rational points on variety, employing various techniques arising from number theory and algebraic geometry. She is currently studying the distributions of rational points (following Manin's conjecture) on Fano varieties, and definability questions related to finding rational points on varieties.
STEFAN PATRIKIS works in number theory and arithmetic geometry, with an emphasis on questions arising out of the Langlands program. His current work focuses on Galois representations: their deformation theory, their monodromy groups and related independence-of-ℓ questions, and their conjectural motivic and automorphic origins.
HSIAN-HUA TSENG's research areas are algebraic and symplectic geometry. His research focuses on Gromov-Witten theory. In particular, he is interested in how various geometric structures on stacks affect Gromov-Witten invariants and connections with other subjects such as integrable systems.
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The Ohio State University, Department of Mathematics, 231 W. 18th Avenue, Columbus, OH, 43210, USA.
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